Stochastic dynamical unit commitment method for power system based on solving quantiles via newton method

ABSTRACT

The disclosure provides a stochastic dynamical unit commitment method for power system based on solving quantiles via Newton method, belonging to power system technologies. The method establishes a unit commitment model with chance constraints for power system parameters. Quantiles of random variables obeying mixed Gaussian distribution is solved by Newton method, and chance constraints are transformed into deterministic linear constraints, so that original problem is transformed into mixed integer linear optimization problem. Finally, the model is solved to obtain on-off strategy and active power plan of units. The disclosure employs Newton method to transform chance constraints containing risk level and random variables into deterministic mixed integer linear constraints, which effectively improves the model solution efficiency, eliminates conservative nature of conventional robust unit commitment, provides reasonable dispatch basis for decision makers. The disclosure is employed to the stochastic and dynamic unit commitment of the power system including large-scale renewable energy grid-connected.

TECHNICAL FIELD

The present disclosure relates to a stochastic dynamical unit commitmentmethod for a power system based on solving quantiles via Newton method,belonging to the field of power system operation technologies.

BACKGROUND

The development and utilization of wind power resources and therealization of energy sustainability are major initiatives in energydevelopment strategy. With the large-scale access of renewable energy tothe power grid, its volatility and stochastic pose two problems for theunit commitment in the power system operation.

On the one hand, an accurate and flexible prediction on an active powerof renewable energy is the basis for realizing the safe and economicalunit commitment. Conventional prediction methods include an intervaldescription method with given upper and lower limits of the activepower, and a description method of simple Gaussian probability densityfunction. Although models such as beta distribution and versatiledistribution, may be also employed in the prediction of the active powerof the renewable energy, they may not accurately fit the renewableenergy to predict the active power, or bring great difficulties forsolution the unit commitment model. Therefore, it needs to employ anaccurate and flexible prediction model.

On the other hand, the volatility and stochastic of the renewable energymake conventional deterministic unit commitment methods difficult to beapplied. Robust models may be feasible. However, due to the conservativenature of robust optimization, it will bring unnecessary costs to thesystem operation. The stochastic unit commitment with chance constraintsis an effective modeling strategy that takes into account systemoperation risk and cost reduction. This method limits the probability ofoccurrence of the risk to a predetermined confidence level, and obtainsthe lowest cost dispatch strategy by minimizing a value of an objectivefunction. However, the existence of random variables in the constraintsmakes the solution of the chance constrained optimization problems verydifficult The existing solution methods generally have the disadvantageof large computational complexity. However, the relaxation solutionmethod makes solution results less accurate and cannot achieve theefficient unit commitment.

In summary, the modeling and rapid solution of the stochastic dynamicalunit commitment considering the stochastic of the active power of therenewable energy is still a major problem affecting the utilization ofrenewable energy.

SUMMARY

The object of the present disclosure is to propose a stochasticdynamical unit commitment method for a power system based on solvingquantiles via Newton method. An active power of renewable energy isaccurately fitted based on mixed Gaussian distribution, and quantiles ofrandom variables may be solved based on Newton method, therebytransforming chance constraints into deterministic mixed integer linearconstraints, which makes full use of the advantages of stochastic unitcommitment with chance constraints, effectively reduces the system riskand saves the cost of power grid operation.

The stochastic dynamical unit commitment method for a power system basedon solving quantiles via Newton method may include the following steps.

(1) A stochastic dynamical unit commitment model with chance constraintsbased on solving quantiles of random variables via Newton method isestablished. The stochastic and dynamic unit commitment model includesan objective function and constraints. The establishing may include thefollowing steps.

(1-1) The objective function of the stochastic dynamical unit commitmentmodel with chance constraints based on solving quantiles of randomvariables via Newton method is established.

The objective function is to minimize a sum of power generation costsand on-off costs of thermal power generating units. The objectivefunction is denoted by a formula of:

${\min {\sum\limits_{t = 1}^{T}\; \left\lbrack {\sum\limits_{i = 1}^{N_{G}}\; \left( {{{CF}_{i}\left( P_{i}^{t} \right)} + {CU}_{i}^{t} + {CD}_{i}^{t}} \right)} \right\rbrack}},$

where, T denotes the number of dispatch intervals; N_(G) denotes thenumber of thermal power generating units in the power system; t denotesa serial number of dispatch intervals; i denotes a serial number ofthermal power generating units; P_(i) ^(t) denotes an active power ofthermal power generating unit i at dispatch interval t; CF_(i) denotes afuel cost function of thermal power generating unit i; CU_(i) ^(t)denotes a startup cost of thermal power generating unit i at dispatchinterval t; and CD_(i) ^(t) denotes a shutdown cost of thermal powergenerating unit i at dispatch interval t.

(1-1) The fuel cost function of the thermal power generating unit isexpressed as a quadratic function of the active power of the thermalpower generating unit, Which is denoted by a formula of:

CF_(i)(P_(i) ^(t))=a _(i)(P_(i) ^(t))² +b _(i) P _(i) ^(t) +c _(i),

where, a_(i) denotes a quadratic coefficient of a fuel cost of thermalpower generating unit i; b_(i) denotes a linear coefficient of the fuelcost of thermal power generating unit i; c_(i) denotes a constantcoefficient of the fuel cost of thermal power generating unit i; andvalues of a_(i), b_(i), and c_(i) may be obtained from a dispatchcenter.

The startup cost of the thermal power generating unit, and the shutdowncost of the thermal power generating unit are denoted by formulas of:

CU _(i) ^(t) ≥U _(i)(v _(i) ^(t) −v _(i) ^(t−1))

CU_(i) ^(t)≥0,

CD_(i) ^(t) ≥D _(i)(v _(i) ^(t−1) −v _(i) ^(t))

CD_(i) ^(t)≥0

where, v_(i) ^(t) denotes a state of thermal power generating unit i atdispatch interval t; if v_(i) ^(t)=0, it represents that thermal powergenerating unit i is in an off state; if v_(i) ^(t)=1, it representsthat thermal power generating unit i is in an on state; it is set thatthere is the startup cost when the unit is switched from the off stateto the on stale, and there is the shutdown cost when the unit isswitched from the on state to the off state; U_(i) denotes a startupcost when the thermal power generating unit i is turned on one time; andD_(i) denotes a shutdown cost when the thermal power generating unit iis turned off one time.

(1-2) Constraints of the stochastic dynamical unit commitment model withchance constraints based on solving quantiles of random variables viaNewton method may include the following.

(1-2-1) A power balance constraint of the power system, which is denotedby a formula of:

${{{\sum\limits_{i = 1}^{N_{G}}\; P_{i}^{t}} + {\sum\limits_{j = 1}^{N_{W}}\; w_{j}^{t}}} = {\sum\limits_{m = 1}^{N_{D}}\; d_{m}^{t}}},$

where, P_(i) ^(t) denotes a scheduled active power of thermal powergenerating unit i at dispatch interval t; w_(j) ^(t) denotes a scheduledactive power of renewable energy power station j at dispatch interval t;d_(m) ^(t) denotes a size of load m at dispatch interval t; and N_(D)denotes the number of loads in the power system.

(1-2-2) An upper and lower constraint of the active power of the thermalpower generating unit in the power system, which is denoted by a formulaof:

P _(i) v _(i) ^(t) ≤P _(i) ^(t) ≤P _(i) v _(i) ^(t),

where, P _(i) denotes an active power lower limit of thermal powergenerating unit i; P _(i) an active power upper limit of thermal powergenerating unit i; v_(i) ^(t) denotes the state of thermal powergenerating unit i at dispatch interval t; if v_(i) ^(t)=0, it representsthat thermal power generating unit i is in an on state; and if v_(i)^(t)=1, it represents that thermal power generating unit i is in an offstate

(1-2-3) A reserve constraint of the thermal power generating unit in thepower system, which is denoted by a formula of:

P _(i) ^(t) +r _(i) ^(t+) ≤P _(i) _(i) ^(t)

0≤r _(i) ^(t+) ≤r _(i) ⁺,

P _(i) ^(t) −r _(i) ^(t−) ≥P _(i) v _(i) ^(t)

0≤r _(i) ^(t−) ≤r _(i) ⁻

where, r_(i) ^(t+) denotes an upper reserve of thermal power generatingunit i at dispatch interval t; r_(i) ^(t−) denotes a lower reserve ofthermal power generating unit i at dispatch interval t; r _(i) ⁺ denotesa maximum upper reserve of thermal power generating unit i at dispatchinterval i; r _(i) ⁻ denotes a maximum lower reserve of thermal powergenerating unit i at dispatch interval t; and the maximum upper reserveand the maximum lower reserve may be obtained from the dispatch centerof the power system.

(1-2-4) A ramp constraint of the thermal power generating unit in thepower system, which is denoted by a formula of:

P _(i) ^(t) −P _(i) ^(t−1) ≥−RD _(i) ΔT−(2−v _(i) ^(t) −v _(i) ^(t−1)) P_(i),

P _(i) ^(t) −P _(i) ^(t−1) ≤RU _(i) ΔT+(2−v _(i) ^(t) −v _(i) ^(t−1)) P_(i)

where, RU_(i) denotes upward ramp capacities of thermal power generatingunit i, and RD_(i) denotes downward ramp capacities of thermal powergenerating unit i, which are obtained from the dispatch center; and ΔTdenotes an interval between two adjacent dispatch intervals.

(1-2-5) A constraint of a minimum continuous on-off period of thethermal power generating unit in the power system, and the expression isas follows.

A minimum interval for power-on and power-off switching of the thermalpower generating unit is denoted by a formula of:

${{\sum\limits_{t = k}^{k + {UT}_{i} - 1}\; v_{i}^{t}} \geq {{UT}_{i}\left( {v_{i}^{k} - v_{i}^{k - 1}} \right)}},{{\forall k} = 2},\ldots \;,{T - {UT}_{i} + 1}$${{\sum\limits_{t = k}^{T}\; \left\{ {v_{i}^{t} - \left( {v_{i}^{k} - v_{i}^{k - 1}} \right)} \right\}} \geq 0},{{\forall k} = {T - {UT}_{i} + 2}},\ldots \;,T$${{\sum\limits_{t = k}^{k + {DT}_{i} - 1}\; \left( {1 - v_{i}^{t}} \right)} \geq {{DT}_{i}\left( {v_{i}^{k - 1} - v_{i}^{k}} \right)}},{{\forall k} = 2},\ldots \;,{T - {DT}_{i} + 1}$${{\sum\limits_{t = k}^{T}\; \left\{ {1 - v_{i}^{t} - \left( {v_{i}^{k - 1} - v_{i}^{k}} \right)} \right\}} \geq 0},{{\forall k} = {T - {DT}_{i} + 2}},\ldots \;,T,$

where, UT_(i) denotes a minimum continuous startup period, and DT_(i)denotes a minimum continuous shutdown period.

(1-2-6) A reserve constraint of the power system, which is denoted by aformula of:

${\Pr \left( {{\sum\limits_{i = 1}^{N_{G}}\; r_{i}^{t +}} \geq {{\sum\limits_{j = 1}^{N_{W}}\; w_{j}^{t}} - {\sum\limits_{j = 1}^{N_{W}}\; {\overset{\sim}{w}}_{j}^{t}} + R^{+}}} \right)} \geq {1 - ɛ_{r}^{+}}$${{\Pr \left( {{\sum\limits_{i = 1}^{N_{G}}\; r_{i}^{t -}} \geq {{\sum\limits_{j = 1}^{N_{W}}\; {\overset{\sim}{w}}_{j}^{t}} - {\sum\limits_{j = 1}^{N_{W}}\; w_{j}^{t}} + R^{-}}} \right)} \geq {1 - ɛ_{r}^{-}}},$

where, {tilde over (w)}^(t) _(j) denotes an actual active power ofrenewable energy power station j at dispatch interval t; w^(t) _(j)denotes a scheduled active power of renewable energy power station j atdispatch interval t; R⁺ and R⁻ denote additional reserve demandrepresenting the power system from the dispatch center; ϵ_(r) ⁺ denotesa risk of insufficient upward reserve in the power system; ϵ_(r) ⁻denotes a risk of insufficient downward reserve in the power system; andPr(·) denotes a probability of occurrence of insufficient upward reserveand a probability of occurrence of insufficient downward reserve. Theprobability of occurrence of insufficient upward reserve and theprobability of occurrence of insufficient downward reserve may beobtained from the dispatch center.

(1-2-7) A branch flow constraint of the power system, which is denotedby a formula of:

${\Pr \left( {{{\sum\limits_{i = 1}^{N_{G}}\; {G_{l,i}{\overset{\sim}{P}}_{i}^{t}}} + {\sum\limits_{j = 1}^{N_{W}}\; {G_{l,j}{\overset{\sim}{w}}_{j}^{t}}} - {\sum\limits_{k = 1}^{N_{D}}\; {G_{l,m}d_{m}^{t}}}} \leq L_{l}} \right)} \geq {1 - \eta}$${{\Pr \left( {{{\sum\limits_{i = 1}^{N_{G}}\; {G_{l,i}{\overset{\sim}{P}}_{i}^{t}}} + {\sum\limits_{j = 1}^{N_{W}}\; {G_{l,j}{\overset{\sim}{w}}_{j}^{t}}} - {\sum\limits_{k = 1}^{N_{D}}\; {G_{l,m}d_{m}^{t}}}} \geq {- L_{l}}} \right)} \geq {1 - \eta}},$

where, G_(l,i) denotes a power transfer distribution factor of branch lto the active power of thermal power generating unit i; G_(l,j) denotesa power transfer distribution factor of branch l to the active power ofrenewable energy power station j; G_(l,m) denotes a power transferdistribution factor of branch l to load m; each power transferdistribution factor may be obtained from the dispatch center; L_(t)denotes an active power upper limit on branch l; and η denotes a risklevel of an active power on the branch of the power system exceeding arated active power upper limit of the brand), which is determined by adispatcher.

(2) Based on the objective function and constraints of the stochasticand dynamic unit commitment model, the Newton method is employed tosolve quantiles of random variables, which may include the followingsteps.

(2-1) The chance constraints are converted into deterministicconstraints containing quantiles.

A general form of the chance constraints is denoted by a formula of:

Pr(c ^(T) {tilde over (w)} ^(t) +d ^(T) x≤e)≥1−p,

where, c and d denote constant vectors with N_(W) dimension in thechance constraints; N_(W) denotes the number of renewable energy powerstations in the power system; e denotes constants in the chanceconstraints; p denotes a risk level of the chance constraints, which isobtained from the dispatch center in the power system; {tilde over(w)}^(t) denotes an actual active power vector of all renewable energypower stations at dispatch interval t; and x denotes a vector consistingof decision variables, and the decision variables are scheduled activepowers of the renewable energy power stations and the thermal powergenerating units.

The above general form of the chance constraints is converted to thedeterministic constraints containing the quantiles by a formula of:

${{e - {d^{T}x}} \geq {{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)}},{where},{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)}$

denotes quantiles when a probability of one-dimensional random variablesc^(T){tilde over (w)}^(t) is equal to 1−p.

(2-2) A joint probability distribution of the actual active powers ofall renewable energy power stations in the power system is set tosatisfy the following Gaussian mixture model:

${\overset{\sim}{w}}^{t} = \left\{ {{\overset{\sim}{w}}_{j}^{t}{1 \leq j \leq N_{W}}} \right\}$${{{PDF}_{{\overset{\sim}{w}}^{t}}(Y)} = {\sum\limits_{s = 1}^{n}\; {\omega_{s}{N\left( {Y,\mu_{s},\Sigma_{s}} \right)}}}},{\omega_{s} \geq 0}$${{N\left( {{Y\mu_{s}},\Sigma_{s}} \right)} = {\frac{1}{\left( {2\pi} \right)^{N_{W}\text{/}2}\mspace{14mu} {\det \left( \Sigma_{s} \right)}^{1\text{/}2}}e^{{- \frac{1}{2}}{({Y - \mu_{s}})}^{T}{\Sigma_{s}^{- 1}{({Y - \mu_{s}})}}}}},$

where, {tilde over (w)}^(t) denotes a set of scheduled active powers ofall renewable enemy power stations in the power system; {tilde over(w)}^(t) is a stochastic vector;

${PDF}_{{\overset{\sim}{w}}_{t}}( \cdot )$

denotes a probability density function of the stochastic vector; Ydenotes values of {tilde over (w)}^(t); N(Y,μ_(s),Σ_(s)) denotes thes^(-th) component of the mixed Gaussian distribution; n denotes thenumber of components of the mixed Gaussian distribution; ω_(s) denotes aweighting coefficient representing the s^(-th) component of the mixedGaussian distribution and a sum of weighting coefficients of allcomponents is equal to 1; μ_(s) denotes an average vector of the s^(-th)component of the mixed Gaussian distribution; Σ_(s) denotes a covariancematrix of the s^(-th) component of the mixed Gaussian distribution;det(Σ_(s)) denotes a determinant of the covariance matrix Σ_(s); and asuperscript T indicates a transposition of matrix.

Thus, a nonlinear equation containing the quantiles

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

is obtained as follows:

${{{\sum\limits_{s = 1}^{n}\; {\omega_{s}{\Phi \left( \frac{y - {c^{T}\mu_{s}}}{\sqrt{c^{T}\Sigma_{s}c}} \right)}}} - \left( {1 - p} \right)} = 0},$

where, Φ(·) denotes a cumulative distribution function representing aone-dimensional standard Gaussian distribution; v denotes a simpleexpression representing the quantile;

${y = {{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)}};$

and μ_(s) denotes an average vector of the s^(-th) component of themixed. Gaussian distribution.

(2-3) Employing the Newton method, the nonlinear equation of step (2-2)is iteratively solved to obtain the quantiles

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

of the random variables c^(T){tilde over (w)}^(t). The specificalgorithm steps are as follows.

(2-3-1) Initialization

An initial value of y is set to y₀, which is denoted by a formula of:

y ₀=max(c ^(T)μ_(i) , i∈{1, 2, . . . , N _(W)}).

(2-3-2) Iteration

A value of y is updated by a formula of:

${y_{k + 1} = {y_{k} - \frac{{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k} \right)} - \left( {1 - p} \right)}{{PDF}_{c^{T}{\overset{\sim}{w}}^{t}}\left( y_{k} \right)}}},{where},{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k} \right)}$

denotes quantiles when a probability of one-dimensional random variablesc^(T){tilde over (w)}^(t) is equal to 1−p; y_(k) denotes a value of y ofa previous iteration; y_(k+1) denotes a value of y of a currentiteration, which is to be solved; and

${PDF}_{c^{T}{\overset{\sim}{w}}^{t}}$

denotes a probability density function representing the stochasticvector c^(T){tilde over (w)}^(t), which is denoted by a formula of:

${{PDF}_{c^{T}{\overset{\sim}{w}}^{t}}(y)} = {\sum\limits_{s = 1}^{n}\; {\omega_{s}\frac{1}{\sqrt{2\pi \; c^{T}\Sigma_{s}c}}{e^{- \frac{{({y - {c^{T}\mu_{s}}})}^{2}}{2c^{T}\Sigma_{s}c}}.}}}$

2-3-3) An allowable error of the iterative calculation ϵ is set; aniterative calculation result is judged based on the allowable error. If

${{{{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k + 1} \right)} - \left( {1 - p} \right)}} \leq ɛ},$

it is determined that the iterative calculation converges, and values ofthe quantiles

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

of the random variables are obtained; and if

${{{{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k + 1} \right)} - \left( {1 - p} \right)}} > ɛ},$

it is returned to (2-2-2).

(3) An equivalent form

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

of the chance constraints in the step (1-2-6) and the step (1-2-7) maybe obtained based on

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

in the step (2); using z branch and bound method, the stochastic unitcommitment model including the objective function and the constraints inthe step (1) is solved to obtain v_(i) ^(t), P_(i) ^(t), and w^(t) _(j).v_(i) ^(t) is taken as a starting and stopping state of thermal powergenerating unit i at dispatch interval t; P_(i) ^(t) is taken as ascheduled active power of renewable energy power station j at dispatchinterval t; and w^(t) _(j) is taken as a reference active power ofrenewable energy power station j at dispatch interval t. Therefore, thestochastic and dynamic unit commitment with chance constraints may besolved based on Newton method for solving quantiles of random variables.

The stochastic dynamical unit commitment method for a power system basedon solving quantiles via Newton method, provided in the presentdisclosure, may have the following advantages.

The method of the present disclosure first accurately describes theactive power characteristics and correlations of renewable energypredictions such as wind power/photovoltaics through the mixed Gaussiandistribution of multiple random variables. Based on the distribution,the method of the present disclosure establishes the stochastic anddynamic unit commitment model with minimum cost expectation byconsidering deterministic constraints and chance constraints. The chanceconstraints limit the safety risk caused by the stochastic of the activepower of the renewable energy power station such as windpower/photovoltaic to the certain confidence level during operation. Atthe same time, the Newton method is used to solve the quantile of therandom variables obeying the mixed Gaussian distribution, thustransforming the chance constraints into the deterministic mixed integerlinear constraints. The stochastic unit commitment model is analyticallyexpressed as the mixed integer quadratic programming model. The resultof the optimization is the optimal dispatch decision of the on-off andactive power of the conventional thermal power unit and the active powerof the renewable energy power station such as wind power/photovoltaic,under the control of operational risk and reduced operating costs. Theadvantage of the method of the present disclosure, is that the Newtonmethod is used to transform the chance constraints containing the risklevel and the random variables into the deterministic mixed integerlinear constraints, which effectively improves the efficiency of solvingthe model. Meanwhile, the model with chance constraints and withadjustable risk level eliminates the conservative nature of theconventional robust unit commitment, to provide a more reasonabledispatch basis for decision makers. The method of the present disclosuremay be employed to the stochastic and dynamic unit commitment of thepower system with large-scale renewable energy integration.

DETAILED DESCRIPTION

The stochastic dynamical unit commitment method for a power system basedon solving quantiles via Newton method, provided by the presentdisclosure, may include the following steps.

(1) A stochastic dynamical unit commitment model with chance constraintsbased on solving quantiles of random variables via Newton method isestablished. The stochastic and dynamic unit commitment model includesan objective function and constraints. The establishing may include thefollowing steps.

(1-1) The objective function of the stochastic dynamical unit commitmentmodel with chance constraints based on solving quantiles of randomvariables via Newton method is established.

The objective function is to minimize a sum of power generation costsand on-off costs of thermal power generating units. The objectivefunction is denoted by a formula of:

${\min {\sum\limits_{t = 1}^{T}\; \left\lbrack {\sum\limits_{i = 1}^{N_{G}}\; \left( {{{CF}_{i}\left( P_{i}^{t} \right)} + {CU}_{i}^{t} + {CD}_{i}^{t}} \right)} \right\rbrack}},$

where, T denotes the number of dispatch intervals; N_(G) denotes thenumber of thermal power generating units in the power system; t denotesa serial number of dispatch intervals; i denotes a serial number ofthermal power generating units; P_(i) ^(t) denotes an active power ofthermal power generating unit i at dispatch interval t; CF_(i) denotes afuel cost function of thermal power generating unit t; CU_(i) ^(t)denotes a startup cost of thermal power generating unit i at dispatchinterval i; and CD_(i) ^(t) denotes a shutdown cost of thermal powergenerating unit i at dispatch interval t.

(1-1) The fuel cost function of the thermal power generating unit isexpressed as a quadratic function of the active power of the thermalpower generating unit, which is denoted by a formula of:

CF _(i)(P _(i) ^(t))=a _(i)(P _(i) ^(t))² +b _(i) P _(i) ^(t) +c _(i).

where, a_(i) denotes a quadratic coefficient of a fuel cost of thermalpower generating unit i; b_(i) denotes a linear coefficient of the fuelcost of thermal power generating unit i; c_(i) denotes a constantcoefficient of the fuel cost of thermal power generating unit i; andvalues of a_(i), b_(i), and c_(i) may be obtained from a dispatchcenter.

The startup cost of the thermal power generating unit, and the shutdowncost of the thermal power generating unit are denoted by formulas of:

CU _(i) ^(t) ≥U _(i)(v _(i) ^(t) −v _(i) ^(t−1))

CU_(i) ^(t)≥0,

CD_(i) ^(t) ≥D _(i)(v _(i) ^(t−1) −v _(i) ^(t))

CD_(i) ^(t)≥0

where, v_(i) ^(t) denotes a state of thermal power generating unit i atdispatch interval i; if v_(i) ^(t)=0, it represents that thermal powergenerating unit i is in an off state; if v_(i) ^(t)=1, it representsthat thermal power generating unit i is in an on state; it is set thatthere is the startup cost when the unit is switched from the off stateto the on state, and there is the shutdown cost when the unit isswitched from the on state to the off state; U_(i) denotes a startupcost when the thermal power generating unit i is turned on one time; andD_(i) denotes a shutdown cost when the thermal power generating unit iis turned off one time.

(1-2) Constraints of the stochastic dynamical unit commitment model withchance constraint based on solving quantiles of random variables viaNewton method may include the following.

(1-2-1) A power balance constraint of the power system, which is denotedby a formula of:

${{{\sum\limits_{i = 1}^{N_{G}}\; P_{i}^{t}} + {\sum\limits_{j = 1}^{N_{W}}\; w_{j}^{t}}} = {\sum\limits_{m = 1}^{N_{D}}\; d_{m}^{t}}},$

where, P_(i) ^(t) denotes a scheduled active power of thermal powergenerating unit i at dispatch interval t; w^(t) _(j) denotes a scheduledactive power of renewable energy power station j at dispatch interval t;d^(t) _(m) denotes a size of load m at dispatch interval t; and N_(D)denotes the number of loads in the power system.

(1-2-2) An upper and lower constraint of the active power of the thermalpower generating unit in the power system, which is denoted by a formulaof:

P _(t) v _(i) ^(t) ≤P _(i) ^(t) ≤P _(i) v _(i) ^(t),

where, P _(t) denotes an active power lower limit of thermal powergenerating unit i; P _(i) an active power upper limit of thermal powergenerating unit i; v_(i) ^(t) denotes the state of thermal powergenerating unit i at dispatch interval t; if v_(i) ^(t)=0, it representsthat thermal power generating unit i is in an on state; and if v_(i)^(t)=1, it represents that thermal power generating unit i is in an offstate.

(1-2-3) A reserve constraint of the thermal power generating unit in thepower system, which is denoted by a formula of:

P _(i) ^(t) +r _(i) ^(t+) ≤P _(i) v _(i) ^(t)

0≤r _(i) ^(t+) ≤r _(i) ⁺,

P _(i) ^(t) −r _(i) ^(t−) ≥P _(i) v _(i) ^(t)

0≤r _(i) ^(t−) ≤r _(i) ⁻

where, r_(i) ^(t+) denotes an upper reserve of thermal power generatingunit i at dispatch interval t; r_(i) ^(t−) denotes a lower reserve ofthermal power generating unit i at dispatch interval t; r _(i) ⁺ denotesa maximum upper reserve of thermal power generating unit i at dispatchinterval t; r _(i) ⁻ denotes a maximum lower reserve of thermal powergenerating unit i at dispatch interval t; and the maximum upper reserveand the maximum lower reserve may be obtained from the dispatch centerof the power system.

(1-2-4) A ramp constraint of the thermal power generating unit in thepower system, which is denoted by a formula of)

P _(i) ^(t) −P _(i) ^(t−1) ≥−RD _(i) ΔT−(2−v _(i) ^(t) −v _(i) ^(t−1)) P_(i),

P _(i) ^(t) −P _(i) ^(t−1) ≤RU _(i) ΔT+(2−v _(i) ^(t) −v _(i) ^(t−1)) P_(i)

where, RU_(i) denotes upward ramp capacities of thermal power generatingunit i, and RD_(i) denotes downward ramp capacities of thermal powergenerating unit ^(i) , which are obtained from the dispatch center; andΔT denotes an interval between two adjacent dispatch intervals.

(1-2-5) A constraint of a minimum continuous on-off period of thethermal power generating unit in the power system, and the expression isas follows.

A minimum interval for power-on and power-off switching of the thermalpower generating unit is denoted by a formula of:

${{\sum\limits_{t = k}^{k + {UT}_{i} - 1}\; v_{i}^{t}} \geq {{UT}_{i}\left( {v_{i}^{k} - v_{i}^{k - 1}} \right)}},{{\forall k} = 2},\ldots \;,{T - {UT}_{i} + 1}$${{\sum\limits_{t = k}^{T}\; \left\{ {v_{i}^{t} - \left( {v_{i}^{k} - v_{i}^{k - 1}} \right)} \right\}} \geq 0},{{\forall k} = {T - {UT}_{i} + 2}},\ldots \;,T$${{\sum\limits_{t = k}^{k + {DT}_{i} - 1}\; \left( {1 - v_{i}^{t}} \right)} \geq {{DT}_{i}\left( {v_{i}^{k - 1} - v_{i}^{k}} \right)}},{{\forall k} = 2},\ldots \;,{T - {DT}_{i} + 1}$${{\sum\limits_{t = k}^{T}\; \left\{ {1 - v_{i}^{t} - \left( {v_{i}^{k - 1} - v_{i}^{k}} \right)} \right\}} \geq 0},{{\forall k} = {T - {DT}_{i} + 2}},\ldots \;,T,$

where, UT_(i) denotes a minimum continuous startup period, and DT_(i)denotes a minimum continuous shutdown period.

(1-2-6) A reserve constraint of the power system, which is denoted by aformula of:

${\Pr \left( {{\sum\limits_{i = 1}^{N_{G}}\; r_{i}^{t +}} \geq {{\sum\limits_{j = 1}^{N_{W}}\; w_{j}^{t}} - {\sum\limits_{j = 1}^{N_{W}}\; {\overset{\sim}{w}}_{j}^{t}} + R^{+}}} \right)} \geq {1 - ɛ_{r}^{+}}$${{\Pr \left( {{\sum\limits_{i = 1}^{N_{G}}\; r_{i}^{t -}} \geq {{\sum\limits_{j = 1}^{N_{W}}\; {\overset{\sim}{w}}_{j}^{t}} - {\sum\limits_{j = 1}^{N_{W}}\; w_{j}^{t}} + R^{-}}} \right)} \geq {1 - ɛ_{r}^{-}}},$

where, {tilde over (w)}^(t) _(j) denotes an actual active power ofrenewable energy power station j at dispatch interval t; w^(t) _(j)denotes a scheduled active power of renewable energy power station j atdispatch interval t; and R⁺ and R⁻ denote additional reserve demandrepresenting the power system from the dispatch center; ϵ_(r) ⁺ denotesa risk of insufficient upward reserve in the power system; ϵ_(r) ⁻denotes a risk of insufficient downward reserve in the power system; andPr(·) denotes a probability of occurrence of insufficient upward reserveand a probability of occurrence of insufficient downward reserve. Theprobability of occurrence of insufficient upward reserve and theprobability of occurrence of insufficient downward reserve may beobtained from the dispatch center.

(1-2-7) A branch flow constraint of the power system, which is denotedby a formula of:

${\Pr \left( {{{\sum\limits_{i = 1}^{N_{G}}\; {G_{l,i}{\overset{\sim}{P}}_{i}^{t}}} + {\sum\limits_{j = 1}^{N_{W}}\; {G_{l,j}{\overset{\sim}{w}}_{j}^{t}}} - {\sum\limits_{k = 1}^{N_{D}}\; {G_{l,m}d_{m}^{t}}}} \leq L_{l}} \right)} \geq {1 - \eta}$${{\Pr \left( {{{\sum\limits_{i = 1}^{N_{G}}\; {G_{l,i}{\overset{\sim}{P}}_{i}^{t}}} + {\sum\limits_{j = 1}^{N_{W}}\; {G_{l,j}{\overset{\sim}{w}}_{j}^{t}}} - {\sum\limits_{k = 1}^{N_{D}}\; {G_{l,m}d_{m}^{t}}}} \geq {- L_{l}}} \right)} \geq {1 - \eta}},$

where, G_(l,i) denotes a power transfer distribution factor of branch lto the active power of thermal power generating unit i; G_(l,j) denotesa power transfer distribution factor of branch l to the active power ofrenewable energy power station j; G_(l,m) denotes a power transferdistribution factor of branch l to load m; each power transferdistribution factor may be obtained from the dispatch center; L_(l)denotes an active power upper limit on branch l; and η denotes a risklevel of an active power on the branch of the power system exceeding arated active power upper limit of the branch, which is determined by adispatcher.

(2) Based on the objective function and constraints of the stochasticand dynamic unit commitment model, the Newton method is employed tosolve quantiles of random variables, which may include the followingsteps.

(2-1) The chance constraints are converted into deterministicconstraints containing quantiles.

A general form of the chance constraints is denoted by a formula of:

Pr(c ^(T) {tilde over (W)} ^(t) +d ^(T) x≤e)≥1−p,

where, c and d denote constant vectors with N_(W) dimension in thechance constraints; N_(W) denotes the number of renewable energy powerstations in the power system; e denotes constants in the chanceconstraints; p denotes a risk level of the chance constraints, which isobtained from the dispatch center in the power system; {tilde over(w)}^(t) denotes an actual active power vector of all renewable enemypower stations at dispatch interval t; and x denotes a vector consistingof decision variables, and the decision variables are scheduled activepowers of the renewable energy power stations and the thermal powergenerating units.

The above general form of the chance constraints is converted to thedeterministic constraints containing the quantiles by a formula of:

${{e - {d^{T}x}} \geq {{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)}},{where},{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)}$

denotes quantiles when a probability of one-dimensional random variablesc^(T){tilde over (w)}^(t) is equal to 1−p.

(2-2) A joint probability distribution of the actual active powers ofall renewable energy power stations in the power system is set tosatisfy the following Gaussian mixture model:

${\overset{\sim}{w}}^{t} = \left\{ {{\overset{\sim}{w}}_{j}^{t}{1 \leq j \leq N_{W}}} \right\}$${{{PDF}_{{\overset{\sim}{w}}^{t}}(Y)} = {\sum\limits_{s = 1}^{n}\; {\omega_{s}{N\left( {Y,\mu_{s},\Sigma_{s}} \right)}}}},{\omega_{s} \geq 0}$${{N\left( {{Y\mu_{s}},\Sigma_{s}} \right)} = {\frac{1}{\left( {2\pi} \right)^{N_{W}\text{/}2}\mspace{14mu} {\det \left( \Sigma_{s} \right)}^{1\text{/}2}}e^{{- \frac{1}{2}}{({Y - \mu_{s}})}^{T}{\Sigma_{s}^{- 1}{({Y - \mu_{s}})}}}}},$

where, {tilde over (w)}^(t) denotes a set of scheduled active powers ofall renewable energy power stations in the power system; {tilde over(w)}^(t) is a stochastic vector;

${PDF}_{{\overset{\sim}{w}}^{t}}( \cdot )$

denotes a probability density function of the stochastic vector; Ydenotes values of {tilde over (w)}^(t); N(Y,μ_(s),Σ_(s)) denotes thes^(-th) component of the mixed Gaussian distribution; n denotes thenumber of components of the mixed Gaussian distribution; ω_(s) denotes aweighting coefficient representing the s^(-th) component of the mixedGaussian distribution and a sum of weighting coefficients of allcomponents is equal to 1; μ_(s) denotes an average vector of the s^(-th)component of the mixed Gaussian distribution; Σ_(s) denotes a covariancematrix of the s^(-th) component of the mixed Gaussian distribution;det(Σ_(s)) denotes a determinant of the covariance matrix Σ_(s) ; and asuperscript T indicates a transposition of matrix.

Thus, a nonlinear equation containing the quantiles

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

is obtained as follows:

${{{\sum\limits_{s = 1}^{n}\; {\omega_{s}{\Phi \left( \frac{y - {c^{T}\mu_{s}}}{\sqrt{c^{T}\Sigma_{s}c}} \right)}}} - \left( {1 - p} \right)} = 0},$

where, Φ(·) denotes a cumulative distribution function representing aone-dimensional standard

Gaussian distribution; y denotes a simple expression representing thequantile;

${y = {{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)}};$

and μ_(s) denotes an average vector of the s^(-th) component of themixed. Gaussian distribution.

(2-3) Employing the Newton method, the nonlinear equation of step (2-2)is iteratively solved to obtain the quantiles

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

of the random variables c^(T){tilde over (w)}^(t). The specificalgorithm steps are as follows.

(2-3-1) Initialization

An initial value of y is set to y₀, which is denoted by a formula of:

y ₀max(c ^(T)μ_(i) ,i∈{1, 2, . . . , N _(W)}).

(2-3-2) Iteration

A value of y is updated by a formula of

${y_{k + 1} = {y_{k} - \frac{{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k} \right)} - \left( {1 - p} \right)}{{PDF}_{c^{T}{\overset{\sim}{w}}^{t}}\left( y_{k} \right)}}},{where},{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k} \right)}$

denotes quantiles when a probability of one-dimensional random variablesc^(T){tilde over (w)}^(t) is equal to 1−p; y^(k) denotes a value of y ofa previous iteration; y_(k+1) denotes a value of y of a currentiteration, which is to be solved; and

${PDF}_{c^{T}{\overset{\sim}{w}}^{t}}$

denotes a probability density function representing the stochasticvector c^(T){tilde over (w)}^(t), which is denoted by a formula of:

${{PDF}_{c^{T}{\overset{\sim}{w}}^{t}}(y)} = {\sum\limits_{s = 1}^{n}\; {\omega_{s}\frac{1}{\sqrt{2\pi \; c^{T}\Sigma_{s}c}}{e^{- \frac{{({y - {c^{T}\mu_{s}}})}^{2}}{2c^{T}\Sigma_{s}c}}.}}}$

(2-3-3) An allowable error of the iterative calculation ϵ is set; aniterative calculation result is judged based on the allowable error. If

${{{{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k + 1} \right)} - \left( {1 - p} \right)}} \leq ɛ},$

it is determined that the iterative calculation converges, and values ofthe quantiles

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

of the random variables are obtained; and if

${{{{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k + 1} \right)} - \left( {1 - p} \right)}} > ɛ},$

it is returned to (2-2-2).

(3) Based on

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

in the step (2), an equivalent form

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

of the chance constraints in the step (1-2-6) and the step (1-2-7). Thechance constraints may exist in both the step (1-2-6) and the step(1-2-7).

${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$

is the result of the general expression of the abstracted chanceconstraints. Therefore, in the same way, the specific expression may beobtained from the abstract expression, thus transforming all the chanceconstraints into the deterministic linear constraints. Since otherconstraints are mixed integer linear constraints on optimizationvariables, the objective function is a quadratic function, and thestochastic unit commitment problem is transformed into an equivalentmixed integer quadratic programming problem. Using the commercialoptimization software CPLEX, and using z branch and bound method, thestochastic unit commitment model including the objective function andthe constraints in the step (1) is solved to obtain v_(i) ^(t), P_(i)^(t), and w^(t) _(j). v_(i) ^(t) is taken as a starting and stoppingstate of thermal power generating unit i at dispatch interval i; P_(i)^(t) is taken as a scheduled active power of renewable energy powerstation j at dispatch interval t; and w^(t) _(j) is taken as a referenceactive power of renewable energy power station j at dispatch interval t.Therefore, the stochastic and dynamic unit commitment with chanceconstraints may be solved based on Newton method for solving quantilesof random variables.

What is claimed is:
 1. A stochastic dynamical unit commitment method fora power system based on solving quantiles via Newton method, comprisingthe following steps: (1) establishing a stochastic dynamical unitcommitment model with chance constraints based on solving quantiles ofrandom variables via Newton method, the stochastic dynamical unitcommitment model comprising an objective function and constraints, theestablishing comprising: (1-1) establishing the objective function ofthe stochastic dynamical unit commitment model with chance constraintsbased on solving quantiles of random variables via Newton method, theobjective function for minimizing a sum of power generating costs andon-off costs of thermal power generating units by a formula of:${\min {\sum\limits_{t = 1}^{T}\; \left\lbrack {\sum\limits_{i = 1}^{N_{G}}\; \left( {{{CF}_{i}\left( P_{i}^{t} \right)} + {CU}_{i}^{t} + {CD}_{i}^{t}} \right)} \right\rbrack}},$where, T denoting the number of dispatch intervals t; N_(G) denoting thenumber of thermal power generating units in the power system; t denotinga serial number of dispatch intervals; i denoting a serial number ofthermal power generating units; P_(i) ^(t) denoting an active power ofthermal power generating unit i at dispatch interval t; CF_(i) denotinga fuel cost function of thermal power generating unit i; CU_(i) ^(t)denoting a startup cost of thermal power generating unit i at dispatchinterval t; and CD_(i) ^(t) denoting a shutdown cost of thermal powergenerating unit i at dispatch interval t; the fuel cost function of thethermal power generating unit being expressed as a quadratic function ofthe active power of the thermal power generating unit by a formula of:CF _(i)(P _(i) ^(t))=a _(i)(P _(i) ^(t))² +b _(i) P _(i) ^(t) +c _(i),where, a_(i) denoting a quadratic coefficient of a fuel cost of thermalpower generating unit; b_(i) denoting a linear coefficient of the fuelcost of thermal power generating unit i; c_(i) denoting a constantcoefficient of the fuel cost of thermal power generating unit; andvalues of a_(i), b_(i), and c_(i) being obtained from a dispatch center;the startup cost of the thermal power generating unit, and the shutdowncost of the thermal power generating unit being denoted by formulas of:CU _(i) ^(t) ≥U _(i)(v _(i) ^(t) −v _(i) ^(t−1))CU_(i) ^(t)≥0,CD _(i) ^(t) ≥D _(i)(v _(i) ^(t−1) −v _(i) ^(t))CD_(i) ^(t)≥0 where, v_(i) ^(t) denoting a state of thermal powergenerating unit i at dispatch interval t; in which, if v_(i) ^(t)=0, itrepresents that thermal power generating unit i is in an off state; ifv_(i) ^(t)=1, it represents that thermal power generating unit i is inan on state; it is set that there is the startup cost when the unit isswitched from the off state to the on state, and there is the shutdowncost when the unit is switched from the on state to the off state; U_(i)denoting a startup cost when thermal power generating unit i is turnedon one time; and D_(i) denoting a shutdown cost when thermal powergenerating unit i is turned off one time; (1-2) obtaining constraints ofthe stochastic dynamical unit commitment model with chance constraintsbased on solving quantiles of random variables via Newton method,comprising: (1-2-1) obtaining a power balance constraint of the powersystem by a formula of:${{{\sum\limits_{i = 1}^{N_{G}}P_{i}^{t}} + {\sum\limits_{j = 1}^{N_{W}}w_{j}^{t}}} = {\sum\limits_{m = 1}^{N_{D}}d_{m}^{t}}},$where, P_(i) ^(t) denoting a scheduled active power of thermal powergenerating unit i at dispatch interval t; w^(t) _(j) denoting ascheduled active power of renewable energy power station j at dispatchinterval t; d^(t) _(m) denoting a size of load in at dispatch intervalt; and N_(D) denoting the number of loads in the power system; (1-2-2)obtaining an upper and lower constraint of the active power of thethermal power generating unit in the power system by a formula of:P _(i) v _(i) ^(t) ≤P _(i) ^(t) ≤P _(i) v _(i) ^(t), where, P _(i)denoting an active power lower limit of thermal power generating unit i;P _(i) denoting an active power upper limit of thermal power generatingunit i; v_(i) ^(t) denoting the state of thermal power generating unit iat dispatch interval t; in which if v_(i) ^(t)=0, it represents thatthermal power generating unit i is in an on state; and if v_(i) ^(t)=1,it represents that thermal power generating unit i is in an off state;(1-2-3) obtaining a reserve constraint of the thermal power generatingunit in the power system, by a formula of:P _(i) ^(t) +r _(i) ^(t+) ≤P _(i) v _(i) ^(t)0≤r _(i) ^(t+) ≤r _(i) ⁺,P _(i) ^(t) −r _(i) ^(t−) ≥P _(i) v _(i) ^(t)0≤r _(i) ^(t−) ≤r _(i) ⁻ where, r_(i) ^(t+) denoting an upper reserve ofthermal power generating unit i at dispatch interval t; r_(i) ^(t−)denoting a lower reserve of thermal power generating unit i at dispatchinterval t; r _(i) ⁺ denoting a maximum upper reserve of thermal powergenerating unit i at dispatch interval t; r _(i) ⁻ denoting a maximumlower reserve of thermal power generating unit i at dispatch interval t;and the maximum upper reserve and the maximum lower reserve beingobtained from the dispatch center of the power system; (1-2-4) obtaininga ramp constraint of the thermal power generating unit in the powersystem, by a formula of:P _(i) ^(t) −P _(i) ^(t−1) ≥−RD _(i) ΔT−(2−v _(i) ^(t) −v _(i) ^(t−1)) P_(i),P _(i) ^(t) −P _(i) ^(t−1) ≤RU _(i) ^(ΔT+)(2−v _(i) ^(t) −v _(i) ^(t−1))P _(i) where, RU_(i) denoting upward ramp capacities of thermal powergenerating unit i, and RD_(i) denoting downward ramp capacities ofthermal power generating unit i, which are obtained from the dispatchcenter; and ΔT denoting an interval between two adjacent dispatchintervals; (1-2-5) obtaining a constraint of a minimum continuous on-offperiod of the thermal power generating unit in the power system,comprising: obtaining a minimum interval for power-on and power-offswitching of the thermal power generating unit by a formula of:${{\sum\limits_{t = k}^{k + {UT}_{i} - 1}\; v_{i}^{t}} \geq {{UT}_{i}\mspace{14mu} \left( {v_{i}^{k} - v_{i}^{k - 1}} \right)}},{{\forall k} = 2},\ldots \;,{T - {UT}_{i} + 1}$${{\sum\limits_{t = k}^{T}\; \left\{ {v_{i}^{t} - \left( {v_{i}^{k} - v_{i}^{k - 1}} \right)} \right\}} \geq 0},{{\forall k} = {T - {UT}_{i} + 2}},\ldots \;,T$${{\sum\limits_{t = k}^{k + {DT}_{i} - 1}\left( {1 - \; v_{i}^{t}} \right)} \geq {{DT}_{i}\mspace{14mu} \left( {v_{i}^{k - 1} - v_{i}^{k}} \right)}},{{\forall k} = 2},\ldots \;,{T - {DT}_{i} + 1}$${{\sum\limits_{t = k}^{T}\; \left\{ {1 - v_{i}^{t} - \left( {v_{i}^{k - 1} - v_{i}^{k}} \right)} \right\}} \geq 0},{{\forall k} = {T - {DT}_{i} + 2}},\ldots \;,T,$where, UT_(i) denoting a minimum continuous startup period, and DT_(i)denoting a minimum continuous shutdown period; (1-2-6) obtaining areserve constraint of the power system by a formula of:${\Pr \left( {{\sum\limits_{i = 1}^{N_{G}}\; r_{i}^{t +}} \geq {{\sum\limits_{j = 1}^{N_{W}}\; w_{j}^{t}} - {\sum\limits_{j = 1}^{N_{W}}\; {\overset{\sim}{w}}_{j}^{t}} + R^{+}}} \right)} \geq {1 - ɛ_{r}^{+}}$${{\Pr \left( {{\sum\limits_{i = 1}^{N_{G}}\; r_{i}^{t -}} \geq {{\sum\limits_{j = 1}^{N_{W}}\; {\overset{\sim}{w}}_{j}^{t}} - {\sum\limits_{j = 1}^{N_{W}}\; w_{j}^{t}} + R^{-}}} \right)} \geq {1 - ɛ_{r}^{-}}},$where, {tilde over (w)}^(t) _(j) denoting an actual active power ofrenewable energy power station j at dispatch interval t; w^(t) _(j)denoting a scheduled active power of renewable energy power station j atdispatch interval t; R⁺ and R⁻ denoting additional reserve demandrepresenting the power system from the dispatch center; ϵ_(r) ⁺ denotinga risk of insufficient upward reserve in the power system; ϵ_(r) ⁻denoting a risk of insufficient downward reserve in the power system;and Pr(·) denoting a probability of occurrence of insufficient upwardreserve and a probability of occurrence of insufficient downwardreserve; the probability of occurrence of insufficient upward reserveand the probability of occurrence of insufficient downward reserve beingobtained from the dispatch center; (1-2-7) obtaining a branch flowconstraint of the power system by a formula of:${\Pr \left( {{{\sum\limits_{i = 1}^{N_{G}}\; {G_{l,i}{\overset{\sim}{P}}_{i}^{t}}} + {\sum\limits_{j = 1}^{N_{W}}\; {G_{l,j}{\overset{\sim}{w}}_{j}^{t}}} - {\sum\limits_{k = 1}^{N_{D}}\; {G_{l,m}d_{m}^{t}}}} \leq L_{l}} \right)} \geq {1 - \eta}$${{\Pr \left( {{{\sum\limits_{i = 1}^{N_{G}}\; {G_{l,i}{\overset{\sim}{P}}_{i}^{t}}} + {\sum\limits_{j = 1}^{N_{W}}\; {G_{l,j}{\overset{\sim}{w}}_{j}^{t}}} - {\sum\limits_{k = 1}^{N_{D}}\; {G_{l,m}d_{m}^{t}}}} \geq {- L_{l}}} \right)} \geq {1 - \eta}},$where, G_(l,i) denoting a power transfer distribution factor of branch lto the active power of thermal power generating unit i; G_(l,j) denotinga power transfer distribution factor of branch l to the active power ofrenewable energy power station j; G_(l,m) denoting a power transferdistribution factor of branch l to load m; each power transferdistribution factor being obtained from the dispatch center; L_(l)denoting an active power upper limit on branch l; and η denoting a risklevel of an active power on the branch of the power system exceeding a.rated active power upper limit of the branch, which is determined by adispatcher; (2) based on the objective function and constraints of thestochastic and dynamic unit commitment model, employing the Newtonmethod to solve quantiles of random variables, comprising: (2-1)converting the chance constraints into deterministic constraintscontaining quantiles, comprising: denoting a general form of the chanceconstraints by a formula of:Pr(c ^(T) {tilde over (w)} ^(t) +d ^(T) x≤e)≥1−p, where, c and ddenoting constant vectors with N_(W) dimension in the chanceconstraints; N_(W) denoting the number of renewable energy powerstations in the power system; e denoting constants in the chanceconstraints; p denoting a risk level of the chance constraints, which isobtained from the dispatch center in the power system; {tilde over(w)}^(t) denoting an actual active power vector of all renewable energypower stations at dispatch interval t; and x denoting a vectorconsisting of decision variables, and the decision variables beingscheduled active powers of the renewable energy power stations and thethermal power generating units; converting the general form of thechance constraints to the deterministic constraints containing thequantiles, by a formula of:${{e - {d^{T}x}} \geq {{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)}},{where},{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)}$denoting quantiles when a probability of one-dimensional randomvariables c^(T){tilde over (w)}^(t) is equal to 1−p; (2-2) setting ajoint probability distribution of the actual active powers of allrenewable energy power stations in the power system to satisfy thefollowing Gaussian mixture model:${\overset{\sim}{w}}^{t} = \left\{ {{\overset{\sim}{w}}_{j}^{t}{1 \leq j \leq N_{W}}} \right\}$${{{PDF}_{{\overset{\sim}{w}}^{t}}(Y)} = {\sum\limits_{s = 1}^{n}\; {\omega_{s}{N\left( {Y,\mu_{s},\Sigma_{s}} \right)}}}},{\omega_{s} \geq 0}$${{N\left( {{Y\mu_{s}},\Sigma_{s}} \right)} = {\frac{1}{\left( {2\pi} \right)^{N_{W}\text{/}2}\mspace{14mu} {\det \left( \Sigma_{s} \right)}^{1\text{/}2}}e^{{- \frac{1}{2}}{({Y - \mu_{s}})}^{T}{\Sigma_{s}^{- 1}{({Y - \mu_{s}})}}}}},$where, {tilde over (w)}^(t) denoting a set of scheduled active powers ofall renewable energy power stations in the power system; {tilde over(w)}^(t) being a stochastic vector;${PDF}_{{\overset{\sim}{w}}^{t}}( \cdot )$ denoting a probabilitydensity function of the stochastic vector; Y denoting values of {tildeover (w)}^(t); N(Y,μ_(s),Σ_(s)) denoting the s^(-th) component of themixed Gaussian distribution; a denoting the number of components of themixed Gaussian distribution; ω_(s) denoting a weighting coefficientrepresenting the s^(-th) component of the mixed Gaussian distributionand a sum of weighting coefficients of all components is equal to 1;μ_(s) denoting an average vector of the s^(-th) component of the mixedGaussian distribution; Σ_(s) denoting a covariance matrix of the S^(-th)component of the mixed Gaussian distribution; det(Σ_(s)) denoting adeterminant of the covariance matrix Σ_(s); and a superscript Tindicating a transposition of matrix; acquiring a nonlinear equationcontaining the quantiles${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$ asfollows:${{{\sum\limits_{s = 1}^{n}\; {\omega_{s}{\Phi \left( \frac{y - {c^{T}\mu_{s}}}{\sqrt{c^{T}\Sigma_{s}c}} \right)}}} - \left( {1 - p} \right)} = 0},$where, Φ(·) denoting a cumulative distribution function representing aone-dimensional standard Gaussian distribution; y denoting a simpleexpression representing the quantile;${y = {{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)}};$and μ_(s) denoting an average vector of the s^(-th) component of themixed Gaussian distribution: (2-3) employing the Newton method, solvingthe nonlinear equation of step (2-2) iteratively to obtain the quantiles${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$ ofthe random variables c^(T){tilde over (w)}^(t), comprising: (2-3-1)initialization: setting an initial value of y to y₀, by a formula of:y ₀=max(c ^(T)μ_(i) ,i∈{1, 2, . . . , N _(W)}); (2-3-2) iteration:updating a value of y by a formula of:${y_{k + 1} = {y_{k} - \frac{{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k} \right)} - \left( {1 - p} \right)}{{PDF}_{c^{T}{\overset{\sim}{w}}^{t}}\left( y_{k} \right)}}},{where},{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k} \right)}$denoting quantiles when a probability of one-dimensional randomvariables c^(T){tilde over (w)}^(t) is equal to 1−p; y_(k) denoting avalue of y of a previous iteration; y_(k+1) denoting a value of y of acurrent iteration, which is to be solved; and${PDF}_{c^{T}{\overset{\sim}{w}}^{t}}$ denoting a probability densityfunction representing the stochastic vector c^(T){tilde over (w)}^(t),which is denoted by a formula of:${{{PDF}_{c^{T}{\overset{\sim}{w}}^{t}}(y)} = {\sum\limits_{s = 1}^{n}\; {\omega_{s}\frac{1}{\sqrt{2\pi \; c^{T}\Sigma_{s}c}}e^{- \frac{{({y - {c^{T}\mu_{s}}})}^{2}}{2c^{T}\Sigma_{s}c}}}}};$(2-3-3) setting an allowable error ϵ of the iterative calculation;judging an iterative calculation result based on the allowable error, inwhich, if${{{{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k + 1} \right)} - \left( {1 - p} \right)}} \leq ɛ},$it is determined that the iterative calculation converges, and values ofthe quantiles${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$ ofthe random variables a obtained; and if${{{{{CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( y_{k + 1} \right)} - \left( {1 - p} \right)}} > ɛ},$it is returned to (2-2-2); (3) obtaining an equivalent form${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$ ofthe chance constraints in the step (1-2-6) and the step (1-2-7) based on${CDF}_{c^{T}{\overset{\sim}{w}}^{t}}^{- 1}\left( {1 - p} \right)$ inthe step (2); using a branch and bound method, solving the stochasticunit commitment model comprising the objective function and theconstraints in the step (1) to obtain v_(i) ^(t), P_(i) ^(t), and w^(t)_(j), in which, v_(i) ^(t) is taken as a starting and stopping state ofthermal power generating unit i at dispatch interval t; P_(i) ^(t) istaken as a scheduled active power of renewable energy power station j atdispatch interval t; and w^(t) _(j) is taken as a reference active powerof renewable energy power station j at dispatch interval t, solving thestochastic and dynamic unit commitment with chance constraints based onsolving quantiles via Newton method.